Related papers: A Jumping Cylinder on an Incline
The purpose of this paper is to compare a classical non-holonomic system---a sphere rolling against the inner surface of a vertical cylinder under gravity---and a class of discrete dynamical systems known as no-slip billiards in similar…
A widely used mathematical model for the bouncing motion of an ideally elastic ball -- referred to in previous work by the first two authors and collaborators as a {\em no-slip billiard} system -- exhibits some notable dynamical behavior…
Complex autonomous driving, such as drifting, requires high-precision and high-frequency pose information to ensure accuracy and safety, which is notably difficult when using only onboard sensors. In this paper, we propose a drift…
The underwater launch of high-speed vehicles involves complex bubble-structure interactions, which are not currently well understood. In this study, two small-scale experiments are carried out involving transient bubble-cylinder…
We revisit the classical problem of the buckling of a long thin axially compressed cylindrical shell. By examining the energy landscape of the perfect cylinder we deduce an estimate of the sensitivity of the shell to imperfections. Key to…
We derive, from the dimensional cross-over criterion, a fundamental-measure density functional for parallel hard curved rectangles moving on a cylindrical surface. We derive it from the density functional of circular arcs of length $\sigma$…
We calculate the friction force acting on a hard cylinder or spherical ball rolling on a flat surface of a viscoelastic solid. The rolling friction coefficient depends non-linearly on the normal load and the rolling velocity. For a cylinder…
We explore the complex dynamics of a non-coalescing drop of moderate size inside a circular hydraulic jump of the same liquid formed on a horizontal disk. In this situation the drop is moving along the jump and one observes two different…
The control of devices with limited input always bring attention to solve by research due to its difficulty and non-trival solution. For instance, the inverted pendulum is benchmarking problem in control theory and machine learning. In this…
The collision of water and elastic liquid drops with a thin cylinder (thread) is studied. The droplet flight trajectory and the cylinder axis are mutually perpendicular. Attention is focused on the difference between collisions of water…
An exact formula is derived, as an integral, for the mean square winding angle of Brownian motion (that is, diffusion) after time t, around an infinitely long impenetrable cylinder of radius a, having started at radius R(>a) from the axis.…
The dynamics and stability of a fluid-filled hollow cylindrical shell rolling on an inclined plane are analyzed. We study the motion in two dimensions by analyzing the interaction between the fluid and the cylindrical shell. An analytical…
We experimentally investigated the melting of floating ice cylinders. Experiments were carried out in a tank, with ice cylinders with radii between 5 cm and 12 cm, floating horizontally with their axis perpendicular to gravity. The water in…
A weak spring is connected at one end to a rotor turning at constant angular velocity. The spring extends to a stretched length as determined by the spring mass, rest length, spring constant, rotor radius and rotor angular velocity. When…
The problem of a disc and a ball rolling on a horizontal plane without slipping is considered. Differential constrained equations are shown to be integrated when the trajectory of the point of contact is taken in a form of the natural…
The problem of a suspended rope wrapped around a fixed cylinder is studied. If the suspension force is larger than a certain threshold (which is larger than the weight of the rope), the rope would remain tightly wrapped around the cylinder.…
An oscillatory instability has been observed experimentally on an horizontal cylinder free to move and rotate between two parallel vertical walls of distance H; its characteristics differ both from vortex shedding driven oscillations and…
We study numerically some possible vortex configurations in a rotating cylinder that is tilted with respect to the rotation axis and where different numbers of vortices can be present at given rotation velocity. In a long cylinder at small…
In the first part of the article using a direct calculation two-dimensional motion of a particle sliding on an inclined plane is investigated for general values of friction coefficient ($\mu$). A parametric equation for the trajectory of…
We examine the dynamics of cylinders that are grooved to form N teeth for rolling motion down an inclined plane. The grooved cylinders are experimentally found to reach a terminal velocity. This result can be explained by the inclusion of…